Antenna Azimuth Position Control System Verification

Antenna Azimuth Position Control System Verification

Dr. Jose Granda

ME270

12/21/07

Graduate Students:Sukhbir Hundal

Bee Thao

Tyrone Tracy

INTRODUCTION:

Control systems are integrated into many facets of life; ranging from nature to social issues to mechanical systems. A nature example would be our bodies: when we want to grab an object, our eyes will focus on it and relay the information to our brain, which will send electrical signals to our muscles to position our arms correctly. There are mechanical systems like controlling water flow from a tank, and keeping the tanks water height at an appropriate height. There are an unlimited number of control examples in the world, but we will focus on a particular electromechanical system. Norman S. Nise investigates the design of a control system for an antenna in his textbook Control Systems Engineering. The name of this project is Antenna Azimuth Position Control System. The basic idea is that someone, from a control tower, can adjust a simple potentiometer by hand and ultimately move a large antenna.

This system is thoroughly analyzed by Dr. Nise. The system schematics are given and transfer functions are obtained by hand. This will provide us support during our analysis of the Antenna Azimuth Position Control System.OBJECTIVE:

Our groups objective is to obtain the same analysis results as the Control Systems Engineering textbook on the same Antenna Azimuth Position Control System. The textbook uses hand analysis, but we will try to match the results using a combination of Camp-G, Matlab, and Simulink. The items we will compare are transfer functions and step responses.

Camp-G should provide the same results as long as our modeling of the system is correct. This is where the hardship may lie. SYSTEM CONCEPT:

We must understand the systems operation so an explanation will follow. Power is applied to a potentiometer. An operator will rotate a potentiometers knob a certain amount. The voltage difference from the source and the new position is then measured. That new voltage signal will be sent to a preamplifier. The preamplifier will amplify the signal by a gain K. Then that result will be sent to a power amplifier. The power amplifier is powered by a much greater voltage to allow for significant gain. So the output of the preamplifier will be amplified by the power amplifier and that result will be sent to a motor. The motor is connected to a shaft and gear #1. Gear #1 is connected to a larger gear #2. Gear #2 is directly connected to the shaft of the antenna. Once the motor powers gear #1 then gear #2 will start to rotate the antenna. Gear #2 is also connected to gear #3. Gear #3 and gear #2 have the same ratio. Gear #3 is connected to another potentiometer. That potentiometer is connected to the same voltage source as the first one. The difference between that potentiometer and the voltage source is then feedback to our original preamplifier. Then the preamplifier will take the difference between the two voltage signals and output that result into the power amplifier. The power amplifier then drives the motor to move the antenna. The process will continue to cycle as long as there is a voltage difference between the two potentiometers in the system. A graphical view is provided by the textbook.

TEXTBOOK SCHEMATIC:

The antenna control system needs to be converted from a physical system to a box diagram schematic. This schematic is provided by the textbook.

Here we can see all parts of our physical system. The potentiometer the operator controls is at the very top. The signal is sent to the preamplifier then to the power amplifier. That result is sent to a motor (gyrator) then to a gear, which is connected to another gear to change the position of the antenna. Finally the antennas signal is connected to another gear and a potentiometer. The feedback is easily seen going back from the potentiometer into the differential preamplifier. The feedback is crucial in determining whether our antenna is in the correct position.

The parameters of the system are given to us by the textbook. We will use the same parameters when comparing results.

Table 1: Schematic Parameters

ANALYSIS:

We will start by breaking down what parts of the system to analyze. There are three main parts: differential preamplifier, power amplifier, and motor plus gears. DIFFERENTIAL PREAMPLIFIER:

The book is very straight forward about this part. They assume that the amplifier never reaches saturation and the dynamics of this part are neglected. This is because the response of this part is typically much faster than the response of the power amplifier. The transfer function of this part is K which is just the gain. Our preamplifier is modeled in CampG:

The textbooks transfer function and step response is shown below:

Our transfer function and step response is shown below:

The two transfer functions and step responses are the same. This was an easy part because all that is happening is a constant gain is applied to a signal.

POWER AMPLIFIER:

The power amplifier takes the output of the preamplifier and amplifies the signal to send to our motor. The op-amp circuit is slightly different than the preamplifier. We had problems with derivative causality in our CampG model so we had to add a C element. The bond graph is shown below:

The textbooks transfer function and step response is shown below:

Our transfer function and step response is shown below:

The transfer function and step responses for both the textbook and our results match closely. We had to adjust resistor and capacitor values in order to obtain the matching transfer functions. This means that our power amplifier should be modeled correctly.

MOTOR AND LOAD:

The motor and load setup has been done several times. The schematic is in the CampG user manual. We started with that one but added an additional TF so that we can account for our systems feedback. The CampG model is shown below:

The textbooks transfer function and step response is shown below:

Our transfer function and step response is shown below:

We put the transfer function the book calculated into Simulink and got a plot. Then we took ours and entered it into Simulink and came up with almost the same exact plot. The slope of the line is different due to the gain of the system.COMPLETE SYSTEM:

Now we must combine all three parts and obtain the systems response. Firstly, our antenna system CampG is shown below:

The textbooks transfer function and step response is shown below:

Our transfer function and step response is shown below:

Once again, we used simulink to compare the results regarding the whole system. Using simulink the transfer function and plot were very similar. Our problem was matching up the Matlab plots.CODING

One of the major issues we had with this project was the Matlab coding. We entered in all the initial conditions that were in the textbook, and then entered in a value for the gyrator, which was not given. After that we would get errors and problems with our results mostly for the Motor analysis and overall system analysis. Finally we figured out that we need to change matrices dimensions in order to obtain 2nd and 3rd order transfer function equations. Still we dont understand the matlab code well enough to match up our calculated transfer function to that one in the book.CONCLUSION

Overall this project was very interesting. It incorporated understanding of several disciplines. A system was given to us that had already been analyzed by hand. We first had to read about the system and conceptually figure out how it was working.

To start the analysis we had to break the system up into a few sections; the differential preamplifier, power amplifier, and motor. Then we continued to model each section with CampG bondgraphs. CampG helped us obtain transfer functions and step responses. We also used simulink to verify these results. Ultimately we compared the textbooks results with ours and found that they were close on some parts and not so close on others. Weve spent many hours on these problems, but are unable to manipulate the Matlab code or system characteristics to obtain the results we want.

One other aspect of this project we spent a lot of time with is physically building the antenna control system on a breadboard. This was very interesting to see the second order/feedback system at work. We had to research all the electrical components of the model and connect everything together. After blowing up several ICs we came up with a working physical model. We have video taped the system in action and included it in the folder that we will turn in.

Looking back we should have started the project a little sooner, but weve learned a lot in a short time, and are confident that we understand the basics of CampG/Matlab/Simulink very well.